The Addition Formulas

Abstract

We now come to an important and fundamental property of the sine and cosine functions. If we know the values of sin α and cos α, and also the values of sin β and cos β, then we can calculate the values of \( \sin (\alpha + \beta ),\cos (\alpha + \beta ),\sin (\alpha - \beta ) \), and \( \cos (\alpha - \beta ) \).